lunarpower wrote:unlike the last question you posted (the number of digits in 2^3000, which would never show up on the gmat), this one, or at least something like it, isn't unreasonable as a test question.

no, you don't have to count.
all that's important in this problem is to find the FIRST and LAST such integers.
unless you've memorized an ungodly number of perfect squares, the latter end will take a bit of experimentation, but it's easy to zero in on the desired value fairly quickly.

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the least such integer is 11^2 = 121. EVERYONE taking the gmat should know perfect squares at this level.

to find the greatest such integer, note that 30^2 = 900, so you know that you're looking for the square of a number that's "a lil bigger than 30".
try them out:
31^2 = 961
32^2 = 1024
so, looks like 31^2 is the upper end.

therefore, you're looking at all the perfect squares from 11^2 to 31^2, inclusive.

there are 31 - 11 + 1 = 21 such perfect squares.
ans (b)